Directional marginal productivity: a foundation of meta-data envelopment analysis

Differential characteristics of the production function represent elasticity measures and marginal rates of production technologies; in particular, marginal productivity (MP) plays an important role in economic theory and applications. This study provides a theoretical foundation of directional marginal productivity (DMP) supporting the meta‐data envelopment analysis (meta‐DEA) which measures the efficiency via marginal‐profit‐maximized orientation. In addition, the segmented marginal rate of technical substitution is developed based on DMP. In fact, DMP is developed to address finding the improving direction of the efficient firm on the frontier towards the marginal profit maximization. This approach, which emphasizes ‘planning’ over ‘efficiency evaluation’, forms the basis for transforming a typical ‘ex‐post’ DEA into an ‘ex‐ante’ DEA study. Two case studies show that the DMP provides an explicit span of directions for productivity improvement via a trade‐off between these distinct directions.